Can I sue for back rent on my succeeded apt? Also what are my rights concerning living in an illegal apt in new york city

I succeeded an illegal apt with no COD from my mother with whom i lived with for over 15 yrs. The last few yrs (3) she withheld rent because of that factor and other problems within the household. That the landlord had yet to correct. 1. Can I sue the landlord for back rent since they knew that this apt was an illegal one since the 60's?
2. what are my legal rights concerning this issue. My mother passed last Dec and I just got a letter today saying I need to reschedule an appointment with the landlords general counsel to discuss my transfer options and occupancy of the mentioned illegal apt. This is the first time i have been contacted by the landlord and I would like to know what my first move should be. I need an legal aid rep but they will not see me till i have an eviction notice